- Trang chủ >>
- Đề thi >>
- Đề thi lớp 1
Bài tập Toán DIFFERENTIATION 22
Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (398.83 KB, 3 trang )
Created by T. Madas
Question 28
A curve has equation
y = x −8 x , x∈» , x ≥ 0 .
The curve meets the coordinate axes at the origin and at the point P .
a) Determine the coordinates of P .
The point Q , where x = 4 , lies on the curve.
b) Find an equation of the normal to curve at Q .
c) Show clearly that the normal to the curve at Q does not meet the curve again.
P ( 64,0 ) , y = x − 16
Created by T. Madas
Created by T. Madas
Question 29
The curve C has equation
y = x3 − 9 x 2 + 24 x − 19 , x ∈ » .
a) Show that the tangent to C at the point P , where x = 1 , has gradient 9 .
b) Find the coordinates of another point Q on C at which the tangent also has
gradient 9 .
The normal to C at Q meets the coordinate axes at the points A and B .
c) Show further that the approximate area of the triangle OAB , where O is the
origin, is 11 square units.
Q ( 5,1)
Created by T. Madas
Created by T. Madas
Question 30
The point A ( 2,1) lies on the curve with equation
y=
( x − 1)( x + 2 ) ,
2x
x∈», x ≠ 0 .
a) Find the gradient of the curve at A .
b) Show that the tangent to the curve at A has equation
3x − 4 y − 2 = 0 .
The tangent to the curve at the point B is parallel to the tangent to the curve at A .
c) Determine the coordinates of B .
gradient at A = 3 , B ( −2,0 )
4
Created by T. Madas
